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Hessian averaging in stochastic Newton methods achieves superlinear convergence
We consider minimizing a smooth and strongly convex objective function using a stochastic Newton method. At each iteration, the algorithm is given an...
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Functional Central Limit Theorem and Strong Law of Large Numbers for Stochastic Gradient Langevin Dynamics
We study the mixing properties of an important optimization algorithm of machine learning: the stochastic gradient Langevin dynamics (SGLD) with a...
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Encounters with Martingales in Stochastic Control
The martingale approach to stochastic control is very natural and avoids some major mathematical difficulties that arise when Hamilton-Jacobi-Bellman...
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An Incentive Algorithm for a Closed Stochastic Network: Data and Mean-Field Analysis
The paper deals with a load-balancing algorithm for a closed stochastic network with two zones with different demands. The algorithm is motivated by...
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Advances in Noise Modeling for Stochastic Systems in Optimal Control
In this paper some noise models for stochastic control systems are described that differ from the well known model of Brownian motion. Some of the...
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Information Structures in Stochastic Dynamic Games and Informational Properties of Equilibria
This chapter deals with information structures and various information structure dependent properties of equilibrium solutions in stochastic dynamic...
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Linear Wave Solutions of a Stochastic Shallow Water Model
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple...
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Stochastic resonance in stochastic PDEs
We consider stochastic partial differential equations (SPDEs) on the one-dimensional torus, driven by space-time white noise, and with a...
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Lp-Estimate for Linear Forward-Backward Stochastic Differential Equations
This paper is concerned with coupled linear forward-backward stochastic differential equations (FBSDEs, for short). When the homogeneous coefficients...
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Optimal execution with stochastic delay
We show how traders use marketable limit orders (MLOs) to liquidate a position over a trading window when there is latency in the marketplace. MLOs...
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Stochastic Control
Stochastic optimal control problems can in principle be solved by stochastic dynamic programming. We pay special attention to the LQG problem where...
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Doubly Reflected Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Coefficients
In this paper, we consider doubly reflected backward stochastic differential equations driven by G -Brownian motion with uniformly continuous...
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Rendering neuronal state equations compatible with the principle of stationary action
The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in...
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Multilevel Techniques for the Solution of HJB Minimum-Time Control Problems
The solution of minimum-time feedback optimal control problems is generally achieved using the dynamic programming approach, in which the value...
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Moderate deviations for systems of slow–fast stochastic reaction–diffusion equations
The goal of this paper is to study the moderate deviation principle for a system of stochastic reaction–diffusion equations with a time-scale...
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A stochastic first-order trust-region method with inexact restoration for finite-sum minimization
We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems....
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An Introduction to Stochastic Team Theory and Solutions to Static Teams
In this chapter, we present a general introduction to stochastic team theory, which may also be viewed as a prelude to Chaps. 3...
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A stochastic representation for the solution of approximated mean curvature flow
The evolution by horizontal mean curvature flow (HMCF) is a partial differential equation in a sub-Riemannian setting with applications in IT and...
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Robust non-zero-sum stochastic differential game of two insurers with common shock and CDS transaction
This paper considers the non-zero-sum stochastic differential game problem between two ambiguity-averse insurers (AAIs) with common shock. Each AAI’s...
